Question

A logic circuit controls the passage of a signal according to the following requirements:
1. Output X will equal to A when control input B and C are same
2. X will remain high when B and C are different.
The logic circuit will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$$\begin{array}{ccc}& ABC& X\\ 0& 000& 0\\ 1& 001& 1\\ 2& 010& 1\\ 3& 011& 0\\ 4& 100& 1\\ 5& 101& 1\\ 6& 110& 1\\ 7& 111& 1\end{array}$$
$X(A,B,C)=\sum m(1,2,4,5,6,7)$

$X=A+\overline{B}C+B\overline{C}$
$=A+B\oplus C$

Alternate Solution:
Consider the circuit of option a

1. For$B=C$
$P=B\oplus C=0$
and $X=A+0=A$
i.e. output X will equal to A when control input B and C are same:
2. For $B\ne C$
$P=B\oplus C=1$
and $X=A+1=1$
i.e., X will remain high when B and C are different, Hence the circuit meets both requirements.